Formulating and solving splittable capacitated multiple allocation hub location problems

It is only recently that good formulations and properties for the basic versions of the hub location problem have become available. Now, versions closer to reality can be tackled with greater guarantees of success. This article deals with the case in which the capacity of the hubs is limited. The focus is on the following interpretation of this capacity: there is, for each hub, an upper bound on the total flow coming directly from the origins. Our problem has the so-called multiple allocation possibility, i.e., there is no hub associated to each node; on the contrary, flows with, say, the same origin but different destinations, can be sent through different routes. Moreover, it is assumed that the flow between a given origin–destination pair can be split into several routes; if this is not the case, the problem becomes quite different and cannot be approached by means of the techniques used in this paper. Tight integer linear programming formulations for the problem are presented, along with some useful properties of the optimal solutions which can be used to speed up the resolution. The computational experience shows that instances of medium size can be solved very efficiently using the new method, which outperforms other methods given in the literature.